Multicollinearity in Multiple Linear Regression: Detection, Consequences, and Remedies

Abstract

Abstract: Multiple linear regression is a widely used statistical tool for modeling relationships between a dependent variable and multiple explanatory variables. However, it assumes that these explanatory variables are independent, which is not always the case in practical scenarios, leading to a phenomenon known as multicollinearity. Multicollinearity occurs when explanatory variables in a regression model are strongly correlated with each other, causing several issues in regression analysis. This paper discusses the detection and remedies for multicollinearity in detail. Detection methods include examining the determinant of the correlation matrix, inspecting correlation coefficients, using partial regression coefficients, calculating Variance Inflation Factors (VIFs), and assessing the condition number and condition index. These techniques help researchers identify the presence and severity of multicollinearity in their dataset. To address multicollinearity, several remedies are proposed, including obtaining more data, dropping collinear variables, using relevant prior information, employing generalized inverses, and employing principal component regression. Ridge regression, which introduces bias to reduce variance, is also discussed as an effective technique to combat multicollinearity. Understanding multicollinearity and employing appropriate detection and remediation strategies is crucial for obtaining reliable and meaningful results from multiple linear regression models